Mr Buckley, from Shoebury in Essex, hadbeen living in Christchurch for a year.
His family told the Echo newspaper they could not afford the GBP5000 (NZD$9663) cost of bringing his body home, and were resigned to missing his cremation in New Zealand.
His mother Gill Ray, a part-time cleaner, said a friend in New Zealand was arranging the ceremony.
"Flying 24 hours to get there, knowing what you're going there for, is not something I want to go through. And of course the cost of flying there is another thing I can't afford," she told the newspaper.
The family had thought Mr Buckley's travel insurance would allow them to bring his body home, but were told because he had been resident in New Zealand for more than six months, it was no longer valid.
"I was really angry about it, but it is hard to think straight at the moment, to be honest," she said.